General HydroStatics
Ship Stability Software 
Command of the Week
(New or interesting aspects of GHS that you may not know about) 
RESIDUAL RATIO LIMIT

The RESIDUAL RATIO LIMIT compares the residual areas of two heel angle ranges, as shown below.
The residual righting arm is measured relative to the heeling arm. The residual area therefore is the area between the absolute righting arm curve and the heeling arm curve for a range of heel angles.
The range in the denominator ends at equilibrium and range in the numerator begins at equilibrium. Therefore, the limit definition for the ratio needs only a starting angle and a terminating angle. The limit syntax allows the lesser of two angles to be taken as the terminating angle. 
This type of limit is used to evaluate a vessel's capability to resist some dynamic situation. The IMO Severe Wind and Roll criterion ensures that there is enough righting energy to resist the combined effect of wind and waves. The heeling moment is due to wind and the starting angle is the result of a wave heeling the vessel to windward. The criterion typically specified a function to determine the rollback angle which is entered with the ROLL command. It only makes sense then that LIMIT provides a ROLL keyword to reference this angle.
Residual area is negative before equilibrium and after the angle of vanishing stability (RA0) because the heeling arm is greater than the absolute righting arm. The residual ratio limit takes the absolute value of the area before equilibrium, but any negative area after RA0 is considered. So if there is any chance that the terminating angles from criterion text might occur after RA0, use multiple limits, each with RA0 as one of the terminating angles: 
LIMIT RESIDUAL RATIO FROM ROLL TO ABS 50 OR RA0 > 1.0
LIMIT RESIDUAL RATIO FROM ROLL TO FLD OR RA0 > 1.0 
Another dynamic situation can occur if a heavy crane load were suddenly lost due to a parted cable. Several crane criteria use the residual ratio to ensure that the potential energy of the counterballast prior to such an event won't capsize the vessel. In this scenario, the starting angle is equilibrium with the crane load is still attached. How might you put that starting angle into a GHS limit? After the initial condition is established and equilibrium found, the hook load is removed without changing the heel angle (no SOLVE). The righting arm curve can then be started from the desired heel angle which is specified as (relative) 0 degrees in the LIMIT. Here is the sequence: 
LIMIT RESIDUAL RATIO FROM 0 TO FLD OR RA0 > 1.4
BOOM "SUSPENDED WEIGHT", 10, 150, 5, 32, 65, 90, 25 SOLVE DELETE "SUSPENDED WEIGHT" RAH /LIM 
Isn't it neat how a (largely) hydrostatic program can be used to address dynamic situations at sea? 
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